Adding Three Linear Time Trends to a Regression with Repeated Time Values

[Eric Czubiak]

Hello,

I am trying to add in three separate yearly linear time trends into a regression. I have data that has events from 1984-2013 with some events occurring multiple times per year. I am trying to separate the trends by three different waves: (1984-1989), (1990-1999), and (2000-2013). Does anyone know how I can go about to do this? I am unable to use the command tsset due to an error of "repeated values in my sample." Another option I thought would work would be to define three dummy variables for each wave and include that into my regression, but I am unsure that the dummy variable method will capture the effect of a linear time trend.

Best,
Eric C.

[Eric Czubiak]

An additional piece of information I forgot to include was that I do not have observations for the years 1988-1990, 2009, or 2012

[William Lisowski]

Here's the basis to an approach for including three separate yearly trends. Background information from help factor variables to understand what this is doing. I think adding ibn.wave#c.year to your independent variables will give you three time trend lines. But view this response as advice on the Stata mechanics, not on the statistics. Further disclaimer is that there are more sophisticated ways of doing this that yield a single trend line with bends in it, but that too is beyond the scope of this response.

clear
input year
1984
1985
1986
1987
1991
1992
1993
1994
1995
1996
1997
1998
1998
2000
2001
2002
2003
2004
2005
2005
2007
2010
2011
2013
end
generate wave = .
replace wave=1 if year<=1989
replace wave=2 if year>1989 & year<=1999
replace wave=3 if year>1999
list year wave ibn.wave#c.year, sepby(wave) noobs

[Clyde Schechter]

One remark about William's good advice. His model including year, wave, and their interaction produces three separate trend lines, one for each of the waves. In some situations, however, the expectation would be that the lines should meet at the boundaries of adjacent waves, so that overall the trend line bends at wave boundaries but remains connected. The contrary situation, implemented in William's model, is that in addition to a change in direction as we move from one wave to the next, there can also be a "shock" or "bump" that resets the baseline at that time. Which model is more appropriate depends on your specific situation.

If you want a trend line that bends but has no jumps at wave boundaries have a look at linear spines, -help mkspline-.

[William Lisowski]

Clyde - Many thanks for filling in the gap in my response, and pointing us to mkspline. That prompted me to read the help file and realize mkspline is substantially different than my previous experience with splines using JMP. It would be really easy to use mkspline for the purpose I was grasping at that you described well.